Dyadic Regression with Sample Selection

TL;DR

This paper develops a new dyadic regression estimator that accounts for sample selection and zero outcomes, providing better inference in network data with dyadic dependence.

Contribution

It extends Kyriazidou's approach to dyadic data, characterizes the estimator's asymptotic distribution, and introduces bias correction methods for improved inference.

Findings

Estimator performs well in finite samples.

Bias correction improves confidence interval accuracy.

Method effectively handles zero-inflated dyadic data.

Abstract

This paper addresses the sample selection problem in panel dyadic regression analysis. Dyadic data often include many zeros in the main outcomes due to the underlying network formation process. This not only contaminates popular estimators used in practice but also complicates the inference due to the dyadic dependence structure. We extend Kyriazidou (1997)'s approach to dyadic data and characterize the asymptotic distribution of our proposed estimator. The convergence rates are $\sqrt{n}$ or $\sqrt{n^{2}h_{n}}$, depending on the degeneracy of the H\'{a}jek projection part of the estimator, where $n$ is the number of nodes and $h_{n}$ is a bandwidth. We propose a bias-corrected confidence interval and a variance estimator that adapts to the degeneracy. A Monte Carlo simulation shows the good finite sample performance of our estimator and highlights the importance of bias correction in both asymptotic regimes when the fraction of zeros in outcomes varies. We illustrate our procedure using data from Moretti and Wilson (2017)'s paper on migration.